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Telegraph Post

Help with maths problem!?

A bird is sitting on top of a telegraph post.
The post is 12 metres high. The bird sees a worm in the ground.
The angle of depression from the bird to the worm is 50 degrees.

a) Calculate the distance of the worm from the bottom of the telegraph post.

b) How far is the bird from the worm?

Draw a 50-90-40 triangle.
The side opposite the 50 degree angle has length 12.
Let x be the distance of the worm to the bottom of the telegraph pole.
Then we have:
tan40 = x / 12
So that x = 10 meters.

Let c be the distance from the bird to the worm. This is the hypotenuse of the triangle, and since it is a right triangle, we may use Pythagoras' Theorem:

10^2 + 12^2 = c^2
Which implies that c = 15.6 meters.

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